Conformations and Their Symmetry

There is another type of symmetry element that, though less common than simple planes and axes, is nonetheless useful. If a molecule has a center of symmetry (symbol i, located at its center of mass), every atom in the structure has an indistinguishable companion atom located the same distance from the center, along a line through the center connecting the atoms. Though it lacks any planes or axes of symmetry, structure 4-6 has a center of symmetry. Do you see how each pair of companion atoms (carbons, hydrogens, chlorines, and bromines) are equivalent by virtue of the i  

It will turn out in Chapter 5 that the actual Hand l3CNMR spectra of toluene match quite closely our expectations for structure A, with one important exception. We find that the three methyl hydrogens always prove to be equivalent. Why is this so The answer lies in the rate at which the ring-methyl bond rotates. Because this process is extremely rapid on the NMR time scale (Section 1.4), the methyl group behaves as 

the methyl group can be treated as if it has threefold symmetry, without regard to the rest of the molecule. But remember, this is true only because of the high rate of rotation. If this rate of interconversion between the conformations were slow on the NMR time scale, we would indeed expect to see multiple H signals from the methyl group hydrogens. 

To summarize, different conformations of a molecule can exhibit different NMR spectroscopic properties. However, if the conformations interconvert rapidly (as they normally do), they generate a time-averaged spectrum that reflects the most symmetrical conformation of the molecule. In order to observe spectra of the separate conformations, it would be necessary to slow down the rotation of some of the single bonds in the molecule, and this can sometimes be done by cooling the sample to a very low temperature. There will be more about these dynamic processes in Chapter 10. 

43 HOMOTOPIC, ENANTIOTOPIC, AND Structures 4-8 and 4-9 are more challenging examples  

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FIGURE 11. (a) Possible silicocene conformers and their symmetry notation, (b) (Hel) PE spectrum (6-10 eV) of bis(j)5-pentamethylcyclopentadienyl)silicon with Koopmans assignment, IE = gMNDO for tjje most j)5d conformer and (c) comparison of radical cation states with analogous Ge and Sn pentamethylcyclopentadienyl sandwiches... 

Figure 25. Calix(4]arene 1,3-diethers with chiral ether residues possible conformations and their symmetry.

The molecular structures of the heptamers of both allotropic forms are nearly the same. The molecules have a chair conformation and their symmetry is close to Cs, but the site symmetry is actually Ci due to intermolecular interactions. Four neighboring atoms [84 to 87 in Fig. 3] are located in a plane in consequence, the torsion angle is close to the unfavorable value of 0° (motif H—1-0—I—). The large internuclear distance of the bond 86-87 is the result of the repulsion of the 3p lone-pairs at these two atoms [21, 74]. 

If we examine equations (1.27)-(1.29), we see that the MOs have exactly the same form as those for HHe or HLi except that one AO has been replaced by a combination of hydrogen AOs. We can thus regard the MOs of CH4 as being formed in this way from one of the carbon AOs and a symmetry orbital (SO) composed of a combination of hydrogen AOs that conforms to the molecular symmetry. In other words, we start by replacing the four hydrogen AOs a-d, which do not have the right symmetry properties for our problem, with an equivalent set of four linear combinations that do. Since any linear function of the I5 AOs can obviously be written as a linear function of the four SOs, the AOs and SOs are clearly equivalent. The SOs and their symmetry properties are indicated in Table 1.2. 

It is quite evident that the ferrous complexes of porphyrins, both natural and synthetic, have extremely high affinities towards NO. A series of iron (II) porphyrin nitrosyls have been synthesized and their structural data [11, 27] revealed non-axial symmetry and the bent form of the Fe-N=0 moiety [112-116]. It has been found that the structure of the Fe-N-O unit in model porphyrin complexes is different from those observed in heme proteins [117]. The heme prosthetic group is chemically very similar, hence the conformational diversity was thought to arise from the steric and electronic interaction of NO with the protein residue. In order to resolve this issue femtosecond infrared polarization spectroscopy was used [118]. The results also provided evidence for the first time that a significant fraction (35%) of NO recombines with the heme-Fe(II) within the first 5 ps after the photolysis, making myoglobin an efficient N O scavenger. 

We should also be familiar with the meaning of the term conformational asymmetry. We know that different conformations of the same compound have different symmetry and different statistical contribution (i.e., their percentage content is different). Therefore, the total effect on the polarization of light depends on the arrangement of atoms in different conformations and also on the statistical contribution of each conformation. This is called conformational asymmetry. The compound CH3-CH2-CH (CH3)C1 has conformational asymmetry because two identical atoms (c) are situated at the asymmetric centre. This compound has three staggered conformations. 

CA of Polysaccharides. Polysaccharides adopt a wide variety of shapes that depend on their composition and their environment. In solution, polymers are almost always random coils that have local regions that might be similar to conformations that are found in the solid state. The chapter by Brant and Christ discusses conformations of polysaccharides in solutions both in terms of these local regions and by the overall shape of the random coil in terms of end-to-end distance, etc. The following discussion concerns only linear (unbranched) molecules, and refers only to regular polymers, i.e., those that have repeated sequences of monomeric residues located by screw-axis (helical) symmetry. 

The partially hydrogenated ring of dihydtocorannulene constitutes a 1,3-cyclo-hexadiene ring, a system that has been well-studied with respect to its geometry and the conformational preferences of substituents. However, the curvature of the corannulene surface introduces an additional stereochemical factor that makes the conformational analysis especially interesting. 1,3-Cyclohexadiene (23) and 9,10-dihydrophenanthrene (24) serve as models they are structurally similar systems, and their stereochemistry and conformational preferences are well documented in the literature. In both cases, the reduced ring adopts a nonplanar, semi-chair conformation of symmetry. 

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